Question

Which is a better offer: two successive discounts of 20% and 5% or a single discount of 25%? Give reasons 

Answer 1

Hi there!
Here's the answer:

¶¶¶ First let us find equivalent discount of successive discounts of 20% and 5%

Let marked price be x

Now apply two successive discounts of 20% and 5%

%Discount = 20%
Discount price= Marked price(1-%Discount)
= x(1-(20/100))
= x(80/100)
= 0.8x
This is price 1

To this again 5% discount is availed.
%Discount= 5%
Discount price= price1(1-%Discount)
= 0.8x(1-(5/100))
= 0.8x(0.95)
= 0.76x
This is price2 or final price.

Now, find equivalent discount to successive discounts of 10%,5%.
Let equivalent discount be d
0.76x = x - d% of x
=> d% of x = x-0.76x
=>(d/100)×x= 0.24x
=> d/100= 0.24
=> d= 0.24×100
•°• d= 24

•°• Effective %discount availed on successive discounts of 10%,5% is 24%.

¶¶ ¶The other is a single discount of 25%.

Clearly, Single discount of 25% is better than two successive discounts of 10% and 5%.


:)
Hope it helps